A lot depends on how old you are: amount of sleep required tends to reduce with age. Disrupted sleep patterns can still result in problems, however.
From personal experience, I found that when I was an undergrad and my hours were all over the place due to a complete absence of organisational skills, 'all-nighters' were the only way to get things done, usually the day before things were due in, and on occasion the day after

(On one occasion, a double all-nighter, followed by a birthday night out, meant about 60 hours with little or no sleep, I thought I was close to death, and probably was)
I discovered that half-hour power naps made me wake up feeling like absolute crap, but that I could actually survive for longer after a short 'waking up' period of staring at a wall and shivering. Ah, good times....
So yeah, anecdotally, power naps seemed to help me quite a lot. I also found that if I
had to stay up, it was far harder on me than if I
chose to stay up. Nightshifts were horrible - I had a knack of closing my eyes so no-one noticed, but then waking up shouting "Gah!" and making everyone, including myself, jump.
Not a massive amount of work has been done on power naps, AFAIK. I found this study, which I haven't read yet, but which looked into prevalence and effect of power napping, which perhaps you might find interesting:
http://www.findarticles.com/p/articles/mi_m0GDQ/is_2_27/ai_81390108
A former lecturer of mine, Bob Hockey (then at the University of Hull), did some work on the effects of sleep deprivation for the European Space Agency. I only have my recollection of his lecture and a short conversation with him, and at the moment I can't seem to find a reference, but he summed his findings up, in a very tiny TARDIS-like nutshell, as indicating that ability to perform complex tasks was largely unaffected by sleep deprivation, but that the ability to cope with an added stressor was markedly affected: so for instance, sleep-deprived subjects could still operate a complex control panel with similar efficiency to rested ones, but as soon as a simulated stressor was introduced (e.g. an alarm going off, and an extra thing to think about), everything went downhill for the people who had had no sleep.
Sleep disruption is an important aspect of depression, one of those vicious circles: people who are depressed often have disrupted sleep, but disrupted sleep can make your mood suffer... etc.